转子系统的动力学“临界跟随”特征及其试验验证

周旋; 廖明夫; 侯理臻; 朱东华; 王瑞; 景琰婷

doi:10.13224/j.cnki.jasp.20230690

转子系统的动力学“临界跟随”特征及其试验验证

doi: 10.13224/j.cnki.jasp.20230690

周旋^1,,
廖明夫^1,*, ,,
侯理臻²,
朱东华²,
王瑞¹,
景琰婷¹

1.
西北工业大学动力与能源学院，西安 710129
2.
中国航天科技集团有限公司西安航天动力研究所，西安 710100

基金项目: 国家科技重大专项（2017-Ⅳ-0001-0038）

详细信息

作者简介:
周旋（1984-），女，博士生，研究领域为转子动力学

通讯作者:
廖明夫（1960-），男，教授，博士，研究领域为航空发动机转子动力学、风能工程。E-mail：mfliao@nwpu.edu.cn

中图分类号: V231.96
计量
- 文章访问数: 29
- HTML浏览量: 16
- PDF量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2023-11-02
- 网络出版日期: 2024-03-04

Characteristics and experimental verification of “critical following speed” on rotor system

1.
School of Power and Energy，Northwestern Polytechnical University，Xi’an 710129，China
2.
Xi’an Aerospace Propulsion Institute，China Aerospace Science and Technology Corporation，Xi’an 710100，China

摘要

摘要:
为了深入探究转子系统“临界跟随”现象的机理，建立悬臂转子模型，分析“临界跟随”状态下的转子动力学特性，设计搭建了悬臂转子试验器，并在高速超转试验台上进行试验验证。研究结果表明：当直径转动惯量与极转动惯量相等时，从一定的转速开始，盘的振动摆角响应会随转速持续增大；具有“临界跟随”特征的模态振型表现为，直径转动惯量与极转动惯量相等的盘位于振型节点，在不平衡力矩作用下，盘心振动位移为零，但盘的摆角不为零且随转速增加而增大，其相位角维持不变；若转子结构并非简单的单盘，则需计算组件的直径转动惯量与极转动惯量，以此检验是否会出现“临界跟随”；考虑转轴质量时，盘的惯量符合直径转动惯量与极转动惯量相等时，不会出现“临界跟随”现象，但会出现自振频率在较宽的范围与转子转速靠近，使“共振”区域变宽；“临界跟随”使得转子对不平衡激励非常敏感，应在转子动力学设计时予以避免。
- 临界跟随 /
- 试验验证 /
- 陀螺效应 /
- 悬臂转子 /
- 固有频率
Abstract:
In order to deeply investigate the mechanism of “critical following speed”, a cantilever rotor dynamic model was established. The dynamic characteristics of the rotor system under “critical following speed” were analyzed. The cantilever rotor experimental system was designed and established, and experimental verification was finished on the overspeed test bench. The analysis results showed that from a certain rotational speed, when the diameter rotational inertia was equal to polar rotational inertia, the vibration pendulum angle response of the disk increased with the increasing rotational speed. The characteristics of the mode shape under “critical following speed” lied in that the disk (diameter rotational inertia was equal to polar rotational inertia) was located at the node of mode shape. The vibration displacement of the disk center was 0, but the pendulum angle of the disk was not 0 and increased with the increasing rotational speed, and the phase angle was kept constant. If the rotor was not a single-disk structure, the diameter rotational inertia and polar rotational inertia of the component should be calculated to determine whether the “critical following speed” phenomenon occurred. Considering the mass of the rotating shaft, when the disk satisfied the condition which diameter rotational inertia was equal to polar rotational inertia, the phenomenon of “critical following speed” did not occur, and the natural frequency line could be close to the speed line within a wide range, which would widen the “resonance vibration” region. “critical following speed” made vibration extremely sensitive to unbalanced load, which should be avoided in rotor dynamics design.
- critical follower speed /
- experimental verification /
- gyroscopic effect /
- cantilever rotor /
- natural frequency

HTML

图 1 悬臂转子动力学模型

Figure 1. Dynamic model of cantilever rotor

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图 2 转子系统坎贝尔图

Figure 2. Campbell diagram of rotor system

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图 3 自振频率线上的振型点及其对应的振型

Figure 3. Mode shapes of the points on the natural frequency line

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图 4 转子第1阶和第2阶正进动自振频率线及其斜率随转速的变化

Figure 4. Variations of 1st and 2nd natural frequency and their slopes with rotational speed

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图 5 盘的振动摆角随转速的变化（I_p=I_d）

Figure 5. Disk pendulum angle with the rotational speed （I_p=I_d）

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图 6 转子的坎贝尔图（I_p=2I_d ，I_p=I_d）

Figure 6. Campbell diagram of rotor system （I_p=2I_d and I_p=I_d）

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图 7 转子的前4阶振型（I_p=2I_d，I_p=I_d）

Figure 7. Four-order mode shapes of rotor system （I_p=2I_d and I_p=I_d）

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图 8 超转试验台

Figure 8. Overspeed test bench

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图 9 驱动轴

Figure 9. Actuating shaft

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图 10 试验件结构与几何尺寸（单位：mm）

Figure 10. Structure and geometrical dimension of test rig （unit: mm）

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图 11 试验器转子1

Figure 11. Rotor test rig 1

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图 12 试验转子2

Figure 12. Rotor test rig 2

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图 13 试验转子1的坎贝尔图

Figure 13. Campbell diagram of rotor test rig 1

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图 14 试验转子1的两阶振型

Figure 14. Two-order mode shapes of rotor test rig 1

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图 15 试验转子2的坎贝尔图

Figure 15. Campbell diagram of rotor test rig 2

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图 16 试验转子2的2阶振型

Figure 16. Two-order mode shapes of rotor test rig 2

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图 17 试验转子1上的3个位移传感器

Figure 17. Three displacement sensors on rotor test rig 1

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图 18 试验转子2上的位移传感器

Figure 18. Displacement sensor on rotor test rig 2

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图 19 试验转子1的振动位移响应曲线

Figure 19. Vibration amplitude response curves of rotor test rig 1

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图 20 试验转子1的振动相位响应曲线

Figure 20. Vibration phase response curves of rotor test rig 1

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图 21 试验转子2振动位移响应曲线

Figure 21. Vibration amplitude response curves of rotor test rig 2

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表 1 转子模型参数

Table 1. Parameters of rotor system

参数	数值	参数	数值
L/m	1.0	a/m	0.6
b/m	0.4	D/m	0.03
E/10¹¹ Pa	2.09	H/m	0.2
Δm/kg	0.001	R/m	0.1
m/kg	40.0	I_p/（kg·m²）	0.4
s_b1/10⁶ （N/m）	4.0	s_b2/10⁶ （N/m）	5.0
c_b1/（N·s/m）	200	c_b2/（N·s/m）	200
ρ/（kg/m³）	7870

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表 2 两件试验件的惯量参数

Table 2. Inertia parameters of two rotor test rigs

试验件	质量/ kg	极转动惯量 I_p/（kg·m²）	直径转动惯量 I_d/（kg·m²）	I_p/I_d
试验件1	9.18	0.0173	0.0168	1.02976
试验件2	8.17	0.017	0.206	0.0825

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